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\documentclass{article} \newtheorem{thm}{Theorem} \begin{document} \section{Algebra} We have the Cauchy-Schwarz inequality: \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] where $a_k$ and $b_k$ are real numbers, for any $k$. \section{Calculus} \begin{thm} If $f(x)$ satisfies the following conditions: \begin{enumerate} \item $f(x)$ is continuous on $[a,b]$, \item $f(x)$ is differentiable on $(a,b)$, \end{enumerate} Then there exists $\xi\in(a,b)$ such that $f'(\xi)=\frac{f(b)-f(a)}{b-a}$. \end{thm} \end{document}